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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 77616cb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 77616.eb1 | 77616cb1 | \([0, 0, 0, -3675, -25382]\) | \(62500/33\) | \(2898208760832\) | \([2]\) | \(92160\) | \(1.0828\) | \(\Gamma_0(N)\)-optimal |
| 77616.eb2 | 77616cb2 | \([0, 0, 0, 13965, -198254]\) | \(1714750/1089\) | \(-191281778214912\) | \([2]\) | \(184320\) | \(1.4294\) |
Rank
sage: E.rank()
The elliptic curves in class 77616cb have rank \(0\).
Complex multiplication
The elliptic curves in class 77616cb do not have complex multiplication.Modular form 77616.2.a.cb
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
